Two oscillators in a dissipative bath

Gianluca Rastelli

We study a quantum harmonic oscillator linearly coupled through the position operator to a first bath and through the momentum operator to a second bath yielding an Ohmic–Drude dissipation. We analyse the oscillator's fluctuations as a function of the ratio between the strength of the two couplings, focusing in particular on the situation in which the two dissipative interactions are comparable. Analytic formulas are derived in the relevant regimes corresponding to the low temperature limit and when the Drude high frequency cutoff is much larger than all other frequencies. At low temperature, each bath operates to suppress the oscillator's ground state quantum fluctuations or appearing in the corresponding interaction. When one of the two dissipative interactions dominates over the other, the fluctuations for the coupling operator are squeezed. When the two interactions are comparable, the two baths enter in competition as the two conjugate operators do not commute yielding quantum frustration . In this regime, remarkably, the fluctuations of both two quadratures can be enhanced by increasing the dissipative coupling.

E. B. Davies

Paolo Tombesi

Heiner Kohler, Fernando Sols

We study the dissipative dynamics of a harmonic oscillator which couples linearly through its position and its momentum to two independent heat baths at the same temperature. We argue that this model describes a large spin in a ferromagnet. We find that some effects of the two heat baths partially cancel each other. This leads to unexpected features such as underdamped oscillations and long relaxation times in the strong coupling regime. Such a partial frustration of dissipation can be ascribed to the canonically conjugate character of position and momentum. We compare this model to the scenario where a single heat bath couples linearly to both the position and the momentum of the central oscillator. In that case less surprising behaviour occurs for strong coupling. The dynamical evolution of the quantum purity for a single and a double wave packet is also investigated.

N. G. van Kampen

Lit-Deh Chang, Sudip Chakravarty

The dynamics of a two-state system coupled to the dissipative degrees of freedom of the environment appears in many different contexts. In this paper we have given a general formulation of the problem as well as a detailed comparison of two a priori very different heat baths: (a) a collection of harmonic oscillators coupled to the system, and (b) a collection of fermions coupled to the system. Consideration of such heat baths is motivated by the assertion that the weakly excited states of the environment can be modeled by a collection of elementary excitations following Landau. Our conclusion is that the case of Ohmic dissipation of harmonic-oscillator heat bath is very similar to the fermionic bath, although a crucially important dimensionless parameter \ensuremath{\alpha} assumes a different range of values in the two different cases.